arXiv subjects

Milo Moses

Publications and source records attributed to Milo Moses.

6 recordsLinked to original sources

arXiv2025

An Algebraic Theory of Gapped Domain Wall Partons

The entanglement bootstrap program has generated new quantum numbers associated with degrees of freedom living on gapped domain walls between topological phases in two dimensions. Most fundamental among these are the so-called "parton" quantum numbers, which give rise to a zoo of composite sectors. In this note, we propose a categorical description of partons. Along the way, we make contact with ideas from generalized symmetries and SymTFT.

cond-mat.str-el↗

arXiv2024

Clifford circuits over non-cyclic abelian groups

We present a discussion of the generalized Clifford group over non-cyclic finite abelian groups. These Clifford groups appear naturally in the theory of topological error correction and abelian anyon models. We demonstrate a generalized Gottesman-Knill theorem, stating that every Clifford circuit can be efficiently classically simulated. We additionally provide circuits for a universal quantum computing scheme based on local two-qudit Clifford gates and magic states.

quant-ph↗

arXiv2023

Anyons in a highly-entangled toric xy model

While ostensibly coined in 1989 by Xiao-Gang Wen, the term "topological order" has been in use since 1972 to describe the behavior of the classical xy model. It has been noted that the xy model does not have Wen's topological order since it is also subject a non-topological U(1) gauge action. We show in a sense this is the only obstruction. That is, if gauge invariance is enforced energetically then the $xy$ model becomes purely topologically ordered. In fact, we show that the quantum $xy$ topological order is an infinite lattice limit of Kitaev's quantum double model applied to the group G=Z.

cond-mat.str-el↗

arXiv2023

Endomorphisms of a certain ring of rational functions

We define a ring whose elements are rational functions, whose addition is polynomial multiplication, and whose multiplication is a convolution operation. It is then show that this ring's endomorphisms exhibit a strong classification. Namely, they will all fall in a well structured family, or they will degenerate. This degeneration is classified strongly in terms of roots of unity.

math.AC↗

arXiv2022

Partial Liouville sums over divisors

Using sieves and elementary manipulations, we show that the signs of partial sums of the Liouville function over divisors are in a strong sense equally distributed.

math.NT↗

arXiv2022

Pontryagin Duality for Modules over Compact Discrete Valuation Rings

We establish an analogue of Pontryagin duality for modules over compact discrete valuation rings $R$. Namely, we define the dual of a topological $R$ module to be its continuous $R$-module homomorphisms into $K/R$, the quotient module of the fraction field by its ring of integers. It is established that for locally compact $R$-modules the double dual map is an isomorphism and homeomorphism. Additionally, given a non-topological $R$-module a canonical topology is constructed, uniquely defined so that the double dual map will be injective and continuous. Finally, the functor assigning a module to itself equipped with canonical topology is shown to be fully faithful, allowing one to recontextualize the topological statements in purely algebraic forms.

math.AC↗